The table below shows the results of a survey in which 2600 adults from Country

Question

The table below shows the results of a survey in which 2600 adults from Country A,1121 adults from Country B, and 1063
adults from Country C were asked if human activity contributes to global warming. Complete parts (a), (b), and (c).

Adults who say that human activity contributes to global warming

Country A 62%

country B 87%

country C 91%

a) Construct a 90% confidence interval for the proportion of adults from Country Upper ACountry A who say human activity contributes to global warming.

(b) Construct a 90% confidence interval for the proportion of adults from Country Upper B Country B who say human activity contributes to global warming.

(c) Construct a 90% confidence interval for the proportion of adults from Country Upper CCountry Cwho say human activity contributes to global warming.

Explanation / Answer

Confidence Interval:

P^ (-/+) E

E =zc * sqrt ((p^ *(1-p^))/n)

zc is the critical value for 10% (100% - 90%) level of confidence is 1.645

Question a)

P^ =0.62

n = 2600

0.62 (-/+) (1.645*sqrt((0.62*(1`-0.62))/2600)

= 0.62 (-/+)0.0157

= 0.604 and 0.636

Answer:

The 90% confidence interval is (0.604 and 0.636)

Question b)

P^ =0.87

n = 1121

0.87 (-/+) (1.645*sqrt((0.87*(1`-0.87))/1121)

= 0.87 (-/+)0.0165

= 0.853 and 0.887

Answer:

The 90% confidence interval is (0.853 and 0.887)

Question c)

P^ =0.91

n = 1063

0.91 (-/+) (1.645*sqrt((0.91*(1`-0.91))/1063)

= 0.91 (-/+) 0.0144

= 0.896 and 0.924

Answer:

The 90% confidence interval is (0.896 and 0.924)

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